Simple Parity-Check Bit Computation for Polar Codes

ABSTRACT

Methods and systems described herein are directed to encoding information bits for transmission. The methods can include receiving a set of information bits ( 900 ) and determining a set of parity check bits ( 910 ). The set of information bits is concatenated with the set of parity check bits ( 920 ), and the information bits are polar encoded into a set of information bits and frozen bits ( 930 ). The encoded set of information bits is transmitted to a wireless receiver ( 940 ). In particular embodiments, each parity check bit in the set of parity check bits is the binary sum of the values of all bits in front of it. Other embodiments include generating a set of parity check bits based on a systematic block code on the least reliable bits of the set of information bits. The methods and systems described herein may be applied to 3GPP 5G mobile communication systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to Provisional Application No.62/570,463 filed Oct. 10, 2017, entitled “Simple Parity-Check BitComputation for Polar Codes,” the contents of which are incorporated byreferenced herein.

TECHNICAL FIELD

The present disclosure relates to polar codes in wireless communicationsand, in particular, parity-check bit computation for polar codes.

BACKGROUND

Polar codes, proposed by Arikan [1], are the first class of constructivecoding schemes that are provable to achieve the symmetric capacity ofthe binary-input discrete memoryless channels under a low-complexitySuccessive Cancellation (SC) decoder. However, the finite-lengthperformance of polar codes under SC is not competitive compared to othermodern channel coding schemes such as Low-Density Parity-Check (LDPC)codes and turbo codes. Later, SC List (SCL) decoder is proposed in [2],which can approach the performance of optimal Maximum-Likelihood (ML)decoder. By concatenating a simple Cyclic Redundancy Check (CRC) coding,it was shown that the performance of concatenated polar code iscompetitive with that of well-optimized LDPC and turbo codes. As aresult, polar codes are being considered as a candidate for future FifthGeneration (5G) wireless communication systems.

The main idea of polar coding is to transform a pair of identicalbinary-input channels into two distinct channels of different qualities,one better and one worse than the original binary-input channel. Byrepeating such a pair-wise polarizing operation on a set of 2^(M)independent uses of a binary-input channel, a set of 2^(M)“bit-channels” of varying qualities can be obtained. Some of these bitchannels are nearly perfect (i.e., error free) while the rest of themare nearly useless (i.e., totally noisy). The point is to use the nearlyperfect channel to transmit data to the receiver while setting the inputto the useless channels to have fixed or frozen values (e.g., 0) knownto the receiver. For this reason, those input bits to the nearly uselessand the nearly perfect channel are commonly referred to as frozen bitsand non-frozen (or information) bits, respectively. Only the non-frozenbits are used to carry data in a polar code. Loading the data into theproper information bit locations has direct impact on the performance ofa polar code. An illustration of the structure of a length-8 polar codeis illustrated in FIG. 1.

In general, the set of information bit locations used to carry datavaries with the number of channel uses, or equivalently the code length,N as well as the number of data bits, or equivalently the number ofinformation bit locations, K. However, with the commonly used additivewhite Gaussian noise (AWGN) channel model, for any code length N, ifK₁<K₂, then the information set A₁ with K₁ information bit locations isalways a (proper) subset of the information set A₂ with K₂ informationbit locations. As a result, with AWGN channel, for any given code lengthN, to specify the information sets for all possible number ofinformation bit locations, K, one needs only to store a ranking sequenceS_(N) of bit location indices of length N so that the last (or thefirst, depending on whether the bit-channel qualities are sorted inascending or descending order) K indices in S_(N) is the set ofinformation bit locations if there are K data bits, for any K∈{1, 2, . .. , N}. Such a ranking sequence S_(N) is referred to as the informationsequence or Polar sequence, from which the locations of bit-channels forcarrying any number of data bits K can be derived.

FIG. 2 illustrates the labeling of the intermediate information bitss_(l,i), where l∈{0, 1, . . . , n} and i∈{0, 1, . . . , N−1} duringpolar encoding with N=8. The intermediate information bits are relatedby the following equation:

s_(l + 1, i) = s_(l, i) ⊕ s_(l, i + 2^(l)), for  ${i \in {\{ {{j \in {\{ {0,1,\ldots \mspace{11mu},{N - 1}} \} \text{:}\mspace{14mu} {mod}\mspace{14mu} ( {\lfloor \frac{j}{2^{l}} \rfloor,2} )}} = 0} \} \mspace{14mu} {and}}}\mspace{11mu}$ l ∈ {0, 1, … , n − 1}${s_{{l + 1},{i + 2^{l}}} = s_{l,{i + 2^{l}}}},{{{for}\mspace{14mu} i} \in {\{ {{j \in {\{ {0,1,\ldots \;,{N - 1}} \} \text{:}{mod}\mspace{14mu} ( {\lfloor \frac{j}{2^{l}} \rfloor,2} )}} = 0} \} \mspace{14mu} {and}}}$l ∈ {0, 1, … , n − 1}

with s_(0,i)≡u_(i) be the info bits, and s_(n,i)≡x_(i) be the code bits,for i∈{0, 1, . . . , N−1}.

As mentioned above, the bit-channels indices of a Polar code of anygiven size N can be sorted (e.g., in ascending order) into an indexranking sequence according to their relative qualities or reliabilitieswhen carrying data. Such a sequence that ranks the bit-channel indicesis commonly called an information sequence or a Polar sequence.

In the 5G-NR standard, the information sequence or Polar sequence of aPolar code of any size N, up to a maximum of N_(max), is chosen as asub-sequence of another Polar sequence, denoted by Q₀ ^(N) ^(max) ⁻¹={Q₀^(N) ^(max) , Q₁ ^(N) ^(max) , . . . , Q_(N) _(max) ₋₁ ^(N) ^(max) }, ofbit channel indices for the largest supportable size N_(max), whereN≤N_(max).

This Polar sequence Q₀ ^(N) ^(max) ⁻¹={Q₀ ^(N) ^(max) , Q₁ ^(N) ^(max) ,. . . , Q_(N) _(max) ₋₁ ^(N) ^(max) }, is given by Table 1, where0≤Q_(i) ^(N) ^(max) ≤N_(max)−1 denotes a bit index before Polar encodingfor i=0, 1, . . . , N−1 and N_(max)=1024. The Polar sequence Q₀ ^(N)^(max) ⁻¹ is in ascending order of reliability W(Q₀ ^(N) ^(max) )<W(Q₁^(N) ^(max) )< . . . <W(Q_(N) _(max) ₋₁ ^(N) ^(max) ), where W(Q_(i)^(N) ^(max) ) denotes the reliability of bit index Q_(i) ^(N) ^(max) .

For any code block encoded to N bits, where N≤N_(max) a same Polarsequence Q₀ ^(N-1)={Q₀ ^(N), Q₁ ^(N), Q₂ ^(N), . . . , Q_(N-1) ^(N)} isused, which is a subset or sub-sequence of Polar sequence Q₀ ^(N) ^(max)⁻¹ with all elements {Q_(i) ^(N) ^(max) } of values less than N, orderedin ascending order of reliability W(Q₀ ^(N))<W(Q₁ ^(N))<W(Q₂ ^(N))< . .. <W(Q_(N-1) ^(N)).

TABLE 1 Polar sequence Q₀ ^(N) ^(max) ⁻¹ and its correspondingreliability W(Q_(i) ^(N) ^(max) ⁾ W(Q_(i) ^(N) ^(max) ) Q_(i) ^(N)^(max) 0 0 1 1 2 2 3 4 4 8 5 16 6 32 7 3 8 5 9 64 10 9 11 6 12 17 13 1014 18 15 128 16 12 17 33 18 65 19 20 20 256 21 34 22 24 23 36 24 7 25129 26 66 27 512 28 11 29 40 30 68 31 130 32 19 33 13 34 48 35 14 36 7237 257 38 21 39 132 40 35 41 258 42 26 43 513 44 80 45 37 46 25 47 22 48136 49 260 50 264 51 38 52 514 53 96 54 67 55 41 56 144 57 28 58 69 5942 60 516 61 49 62 74 63 272 64 160 65 520 66 288 67 528 68 192 69 54470 70 71 44 72 131 73 81 74 50 75 73 76 15 77 320 78 133 79 52 80 23 81134 82 384 83 76 84 137 85 82 86 56 87 27 88 97 89 39 90 259 91 84 92138 93 145 94 261 95 29 96 43 97 98 98 515 99 88 100 140 101 30 102 146103 71 104 262 105 265 106 161 107 576 108 45 109 100 110 640 111 51 112148 113 46 114 75 115 266 116 273 117 517 118 104 119 162 120 53 121 193122 152 123 77 124 164 125 768 126 268 127 274 128 518 129 54 130 83 13157 132 521 133 112 134 135 135 78 136 289 137 194 138 85 139 276 140 522141 58 142 168 143 139 144 99 145 86 146 60 147 280 148 89 149 290 150529 151 524 152 196 153 141 154 101 155 147 156 176 157 142 158 530 159321 160 31 161 200 162 90 163 545 164 292 165 322 166 532 167 263 168149 169 102 170 105 171 304 172 296 173 163 174 92 175 47 176 267 177385 178 546 179 324 180 208 181 386 182 150 193 153 184 165 185 106 18655 187 328 188 536 189 577 190 548 191 113 192 154 193 79 194 269 195108 196 578 197 224 198 166 199 519 200 552 201 195 202 270 203 641 204523 205 275 206 580 207 291 208 59 209 169 210 560 211 114 212 277 213156 214 87 215 197 216 116 217 170 218 61 219 531 220 525 221 642 222281 223 278 224 526 225 177 226 293 227 388 228 91 229 584 230 769 231198 232 172 233 120 234 201 235 336 236 62 237 282 238 143 239 103 240178 241 294 242 93 243 644 244 202 245 592 246 323 247 392 248 297 249770 250 107 251 180 252 151 253 209 254 284 255 648 256 94 257 204 258298 259 400 260 608 261 352 262 325 263 533 264 155 265 210 266 305 267547 268 300 269 109 270 184 271 534 272 537 273 115 274 167 275 225 276326 277 306 278 772 279 157 280 656 281 329 282 110 283 117 284 212 285171 286 776 287 330 288 226 289 549 290 538 291 387 292 308 293 216 294416 295 271 296 279 297 158 298 337 299 550 300 672 301 118 302 332 303579 304 540 305 389 306 173 307 121 308 553 309 199 310 784 311 179 312228 313 338 314 312 315 704 316 390 317 174 318 554 319 581 320 393 321283 322 122 323 448 324 353 325 561 326 203 327 63 328 340 329 394 330527 331 582 332 556 333 181 334 295 335 285 336 232 337 124 338 205 339182 340 643 341 562 342 286 343 585 344 299 345 354 346 211 347 401 348185 349 396 350 344 351 586 352 645 353 593 354 535 355 240 356 206 35795 358 327 359 564 360 800 361 402 362 356 363 307 364 301 365 417 366213 367 568 368 832 369 588 370 186 371 646 372 404 373 227 374 896 375594 376 418 377 302 378 649 379 771 380 360 381 539 382 111 383 331 384214 385 309 386 188 387 449 388 217 389 408 390 609 391 596 392 551 393650 394 229 395 159 396 420 397 310 398 541 399 773 400 610 401 657 402333 403 119 404 600 405 339 406 218 407 368 408 652 409 230 410 391 411313 412 450 413 542 414 334 415 233 416 555 417 774 418 175 419 123 420658 421 612 422 341 423 777 424 220 425 314 426 424 427 395 428 673 429583 430 355 431 287 432 183 433 234 434 125 435 557 436 660 437 616 438342 439 316 440 241 441 778 442 563 443 345 444 452 445 397 446 403 447207 448 674 449 558 450 785 451 432 452 357 453 187 454 236 455 664 456624 457 587 458 780 459 705 460 126 461 242 462 565 463 398 464 346 465456 466 358 467 405 468 303 469 569 470 244 471 595 472 189 473 566 474676 475 361 476 706 477 589 478 215 479 786 480 647 481 348 482 419 483406 484 464 485 680 486 801 487 362 488 590 489 409 490 570 491 788 492597 493 572 494 219 495 311 496 708 497 598 498 601 499 651 500 421 501792 502 802 503 611 504 602 505 410 506 231 507 688 508 653 509 248 510369 511 190 512 364 513 654 514 659 515 335 516 480 517 315 518 221 519370 520 613 521 422 522 425 523 451 524 614 525 543 526 235 527 412 528343 529 372 530 775 531 317 532 222 533 426 534 453 535 237 536 559 537833 538 804 539 712 540 834 541 661 542 808 543 779 544 617 545 604 546433 547 720 548 816 549 836 550 347 551 897 552 243 553 662 554 454 555318 556 675 557 618 558 898 559 781 560 376 561 428 562 665 563 736 564567 565 840 566 625 567 238 568 359 569 457 570 399 571 787 572 591 573678 574 434 575 677 576 349 577 245 578 458 579 666 580 620 581 363 582127 583 191 584 782 585 407 586 436 587 626 588 571 589 465 590 681 591246 592 707 593 350 594 599 595 668 596 790 597 460 598 249 599 682 600573 601 411 602 803 603 789 604 709 605 365 606 440 607 628 608 689 609374 610 423 611 466 612 793 613 250 614 371 615 481 616 574 617 413 618603 619 366 620 468 621 655 622 900 623 805 624 615 625 684 626 710 627429 628 794 629 252 630 373 631 605 632 848 633 690 634 713 635 632 636482 637 806 638 427 639 904 640 414 641 223 642 663 643 692 644 835 645619 646 472 647 455 648 796 649 809 650 714 651 721 652 837 653 716 654864 655 810 656 606 657 912 658 722 659 696 660 377 661 435 662 817 663319 664 621 665 812 666 484 667 430 668 838 669 667 670 488 671 239 672378 673 459 674 622 675 627 676 437 677 380 678 818 679 461 680 496 681669 682 679 683 724 684 841 685 629 686 351 687 467 688 438 689 737 690251 691 462 692 442 693 441 694 469 695 247 696 683 697 842 698 738 699899 700 670 701 783 702 849 703 820 704 728 705 928 706 791 707 367 708901 709 630 710 685 711 844 712 633 713 711 714 253 715 691 716 824 717902 718 686 719 740 720 850 721 375 722 444 723 470 724 483 725 415 726485 727 905 728 795 729 473 730 634 731 744 732 852 733 960 734 865 735693 736 797 737 906 738 715 739 807 740 474 741 636 742 694 743 254 744717 745 575 746 913 747 798 748 811 749 379 750 697 751 431 752 607 753489 754 866 755 723 756 486 757 908 758 718 759 813 760 476 761 856 762839 763 725 764 698 765 914 766 752 767 868 768 819 769 814 770 439 771929 772 490 773 623 774 671 775 739 776 916 777 463 778 843 779 381 780497 781 930 782 821 783 726 784 961 785 872 786 492 787 631 788 729 789700 790 443 791 741 792 845 793 920 794 382 795 822 796 851 797 730 798498 799 880 800 742 801 445 802 471 803 635 804 932 805 687 806 903 807825 808 500 809 846 810 745 811 826 812 732 813 446 814 962 815 936 816475 817 853 818 867 819 637 820 907 821 487 822 695 823 746 824 828 825753 826 854 827 857 828 504 829 799 830 255 831 964 832 909 833 719 834477 835 915 836 638 837 748 838 944 839 869 840 491 841 699 842 754 843858 844 478 845 968 846 383 847 910 848 815 849 976 850 870 851 917 852727 853 493 854 873 855 701 856 931 857 756 858 860 859 499 860 731 861823 862 922 863 874 864 918 865 502 866 933 867 743 868 760 869 881 870494 871 702 872 921 873 501 874 876 875 847 876 992 877 447 878 733 879827 880 934 881 882 882 937 883 963 884 747 885 505 886 855 887 924 888734 889 829 890 965 891 938 892 884 893 506 894 749 895 945 896 966 897755 898 859 899 940 900 830 901 911 902 871 903 639 904 888 905 479 906946 907 750 908 969 909 508 910 861 911 757 912 970 913 919 914 875 915862 916 758 917 948 918 977 919 923 920 972 921 761 922 877 923 952 924495 925 703 926 935 927 978 928 883 929 762 930 503 931 925 932 878 933735 934 993 935 885 936 939 937 994 938 980 939 926 940 764 941 941 942967 943 886 944 831 945 947 946 507 947 889 948 984 949 751 950 942 951996 952 971 953 890 954 509 955 949 956 973 957 1000 958 892 959 950 960863 961 759 962 1008 963 510 964 979 965 953 966 763 967 974 968 954 969879 970 981 971 982 972 927 973 995 974 765 975 956 976 887 977 985 978997 979 986 980 943 981 891 982 998 983 766 984 511 985 988 986 1001 987951 988 1002 989 893 990 975 991 894 992 1009 993 955 994 1004 995 1010996 957 997 983 998 958 999 987 1000 1012 1001 999 1002 1016 1003 7671004 989 1005 1003 1006 990 1007 1005 1008 959 1009 1011 1010 1013 1011895 1012 1006 1013 1014 1014 1017 1015 1018 1016 991 1017 1020 1018 10071019 1015 1020 1019 1021 1021 1022 1022 1023 1023

Polar codes may be used with parity check (PC) bits. Because theminimum-distance property of Polar codes is typically not good, an outercode is often used in combination of a polar code to improve itsperformance. The encoder of such a concatenation of Polar code and anouter code is shown in FIG. 3, where the outer code is sometimesreferred to as a Parity Check (PC) code. Such an outer code, or PC code,generates PC bits based on the data bits, in such a way that each PC bitdepends only on the data bits placed before it (but not after it)according to the decoding order in a successive (list) decoder. Thisproperty allows an SCL decoder to take advantage of the knownrelationship between data bits and PC bits to trim the candidate pathsduring list decoding and thus get rid of the erroneously decoded pathsfrom the list of candidate paths, which in turn improves the errorperformance of the decoder. The PC bits are sometimes referred to as PCfrozen bits or dynamic frozen bits in the 5G-NR standard.

Denote Q _(I) ^(N) as a subset of bit indices in Polar sequence Q₀^(N-1), and Q _(F) ^(N) as the subset of other bit indices in Polarsequence Q₀ ^(N-1), where Q _(I) ^(N) denote the indices of bit-channelsused to carry either data bits or parity check bits, and Q _(F) ^(N)denotes the indices of bits channels that are frozen to known values.Thus, we have |Q _(I) ^(N)|=K+n_(PC), |Q _(F) ^(N)|=N−|Q _(I) ^(N)|,where K denotes the number of data bits, and n_(PC) is the number ofparity check bits.

In the 5G-NR standard, the location of the PC bits (i.e., the bitindices associated with these PC bits) are computed as follows: LetG_(N)=(G₂)^(⊗n) denote the n-th Kronecker power of matrix G₂, where

$G_{2} = {\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}.}$

For a bit index j with j=0, 1, . . . , N−1, denote g_(j) as the j-th rowof G_(N) and w(g_(j)) as the row weight of g_(j), where w(g_(j)) is thenumber of ones in g_(j). Denote the set of bit indices for PC bits asQ_(PC) ^(N), where |Q_(PC) ^(N)|=n_(PC). The PC bits are divided intotwo kinds: A number of (n_(PC)−n_(PC) ^(wm)) parity check bits areplaced in the (n_(PC)−n_(PC) ^(wm)) least reliable bit indices in Q _(I)^(N). A number of n_(PC) ^(wm) other parity check bits are placed in thebit indices of minimum row weight in {tilde over (Q)}_(I) ^(N), where{tilde over (Q)}_(I) ^(N) denotes the |Q _(I) ^(N)|−n_(PC)) mostreliable bit indices in Q _(I) ^(N); if there are more than n_(PC) ^(wm)bit indices of the same minimum row weight in {tilde over (Q)}_(I) ^(N),the n_(PC) ^(wm) other parity check bits are placed in the n_(PC) ^(wm)bit indices of the highest reliability and the minimum row weight in{tilde over (Q)}_(I) ^(N).

Generate u=[u₀ u₁ u₂ . . . u_(N-1)] according to the following:

k = 0 ; if n_(PC) > 0  y₀ = 0 ; y₁ = 0 ; y₂ = 0 ; y₃ = 0 ; y₄ = 0 ;  forn = 0 to N −1 y_(t) = y₀ ; y₀ = y₁ ; = y₂ ; y₂ = y₃ ; y₃ = y₄ ; y₄ =y_(t) ; if n ∈ Q _(I) ^(N) if n ∈ Q_(PC) ^(N) u_(n) = y₀ ; else u_(n) =c′_(k); k = k +1 ; y₀ = y₀⊕ u_(n) ; end if else u_(n) = 0 ; end if endfor

In the 5G-NR standard, one possible number of PC bits is 3, i.e.n_(PC)=3. Given the locations of the n_(PC) PC bits, the 5G-NR standardmay compute the values of the PC bits using a length-5 shift register.Specifically, the PC frozen bits value may be generated by a p-length(e.g., p=5) cyclic shift register operation like below:

1. initialize a p-length cyclic shift register, y[0], . . . , y[p−1], to02. go through the elements in [u₀, u₁, u₂, . . . , u_(N-1)],

-   -   cyclic left shift the register: y[i]=y[(i−1) mod p] for i=0, 1,        . . . , p−1.    -   if the i-th sub-channel is information: set y[0]=(u_(i) XOR        y[0])    -   if the i-th sub-channel is PC frozen: set u_(i)=y[0]

SUMMARY Problems with Existing Solutions

There currently exist certain challenge(s). For example, where 3 PC bitsmay typically be used in the concatenation of Polar code and PC outercode, a shift-register computation of length 5 is used. However, asconstructed, the first PC bit does not depend on any info bits and thusreduces to a regular frozen bit in most cases. Even the 2nd PC bit isalso frozen in a significant number of cases. Only the last PC bit isnot frozen in most cases. As a result, the effective number of PC bitsis often much less than 3, and as a result, the performance benefit ofsuch a small number of PC bits, if any, is quite limited.

On the other hand, because the last PC bit is often situated far awayfrom the first info bit, the shift register computation is non-trivialand incurs significant additional delay and computational complexity,which is hard to justify when the performance benefit is negligible.

BRIEF SUMMARY OF SOME EMBODIMENTS OF THE PRESENT DISCLOSURE/SOLUTION

Certain aspects of the present disclosure and their embodiments mayprovide solutions to these or other challenges. Parity Check (PC) bitsgenerated by certain outer code, are often placed at certain knownspecific locations to enhance the performance of SC or SCL decoding ofPolar codes. These PC bits are often data dependent so that the decodercan take advantage of the known relationship of these PC bits with otherdata bits to enhance the Polar code performance. Particular embodimentsinclude simple and effective methods of computing the PC bits. Accordinga particular embodiment, each PC bit is computed by simply performingmodulo-2 addition of all the data bits placed in front of the PC bit.This can be implemented using a size-1 shift register, which is simple.According to another embodiment, all PC bits are functions of K_PC leastreliable PC bits, where K_PC may be a fixed constant or may bedetermined based on the code rate of the Polar code. In a special caseof this embodiment, the PC bits are simply repetition of the K_PC leastreliable PC bits.

Particular embodiments use a simple, low complexity method of couplingsome data bits with a special set of “artificially” known bits calledParity Check (PC) bits. The values of these PC bits are data dependent.Two groups of embodiments are described herein, one summing over allprevious data bit values, and the other summing over a subset of theleast reliable data bits according to a pre-determined parity checkmatrix.

There are, proposed herein, various embodiments which address one ormore of the issues disclosed herein. According to some embodiments, amethod performed by a wireless transmitter for encoding information bitscomprises: receiving a set of information bits; determining a set ofparity check bits; concatenating the set of information bits with theset of parity check bits; Polar encoding the information bits into a setof information bits and frozen bits; and transmitting the encoded set ofinformation bits to a wireless receiver. In particular embodiments, eachparity check bit in the set of parity check bits is the binary sum ofthe values of all bits in front of it (either including or excludingother parity bits in front). Other embodiments include generating a setof parity check bits based on a systematic block code on the leastreliable bits of the set of information bits.

According to some embodiments, a method performed by a wireless receiverfor decoding information bits comprises: receiving a set of polar codedinformation bits concatenated with a set of parity check bits, whereineach parity check bit in the set of parity check bits is determined asdescribed in the embodiments above; decoding the set of polar codedinformation bits concatenated with the set of parity check bits; andterminating the decoding when one of the parity check bits in the set ofparity check bits indicates an error.

Certain embodiments may provide one or more of the following technicaladvantage(s). Particular embodiments improve the error performance ofthe Polar code (e.g., by reducing the block error rate) with littleincrease in computational complexity. Another advantage is to provideearly termination benefits, because any of the PC bits may be used forerror detection.

Various other features and advantages will become apparent to those ofordinary skill in the art, in light of the following written descriptionand accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawing figures incorporated in and forming a part ofthis specification illustrate several aspects of the disclosure, andtogether with the description serve to explain the principles of thedisclosure.

FIG. 1 is an illustration of the structure of a length 8 polar code,according to exemplary embodiments;

FIG. 2 illustrates the labeling of the intermediate information bitswhere l∈{0, 1, . . . , n} and i∈{0, 1, . . . , N−1} during polarencoding with N=8, according to exemplary embodiments;

FIG. 3 illustrates an exemplary encoder of a concatenation of polar codeand an outer parity check code, according to some embodiments of thepresent disclosure;

FIG. 4 illustrates an encoder with a cyclic redundancy check attachment,according to various embodiments;

FIG. 5 illustrates a modified successive cancellation list (SCL) Polardecoder and deinterleaver, according to various embodiments;

FIG. 6 illustrates an exemplary wireless network, according to variousembodiments;

FIG. 7 illustrates example embodiments of a wireless device (or userequipment) in which embodiments of the present disclosure may beimplemented, according to various embodiments;

FIG. 8 illustrates a virtualization environment in accordance withexemplary embodiments;

FIG. 9 illustrates a flowchart showing a method of performing variousfunctions described herein, according to various embodiments;

FIG. 10 illustrates a flowchart showing a method of performing variousfunctions described herein, according to various embodiments;

FIG. 11 illustrates an exemplary virtualization apparatus in accordancewith various embodiments; and

FIG. 12 illustrates an exemplary virtualization apparatus in accordancewith various embodiments.

DETAILED DESCRIPTION

The embodiments set forth below represent information to enable thoseskilled in the art to practice the embodiments and illustrate the bestmode of practicing the embodiments. Upon reading the followingdescription in light of the accompanying drawing figures, those skilledin the art will understand the concepts of the disclosure and willrecognize applications of these concepts not particularly addressedherein. It should be understood that these concepts and applicationsfall within the scope of the disclosure.

Radio Node: As used herein, a “radio node” is either a radio access nodeor a wireless device.

Radio Access Node: As used herein, a “radio access node” or “radionetwork node” is any node in a radio access network of a cellularcommunications network that operates to wirelessly transmit and/orreceive signals. Some examples of a radio access node include, but arenot limited to, a base station (e.g., a New Radio (NR) base station(gNB) in a Third Generation Partnership Project (3GPP) Fifth Generation(5G) NR network or an enhanced or evolved Node B (eNB) in a 3GPP LongTerm Evolution (LTE) network), a high-power or macro base station, alow-power base station (e.g., a micro base station, a pico base station,a home eNB, or the like), and a relay node.

Core Network Node: As used herein, a “core network node” is any type ofnode in a core network. Some examples of a core network node include,e.g., a Mobility Management Entity (MME), a Packet Data Network Gateway(PGW), a Service Capability Exposure Function (SCEF), or the like.

Wireless Device: As used herein, a “wireless device” is any type ofdevice that has access to (i.e., is served by) a cellular communicationsnetwork by wirelessly transmitting and/or receiving signals to a radioaccess node(s). Some examples of a wireless device include, but are notlimited to, a User Equipment device (UE) in a 3GPP network and a MachineType Communication (MTC) device.

Network Node: As used herein, a “network node” is any node that iseither part of the radio access network or the core network of acellular communications network/system.

Note that the description given herein focuses on a 3GPP cellularcommunications system and, as such, 3GPP terminology or terminologysimilar to 3GPP terminology is oftentimes used. However, the conceptsdisclosed herein are not limited to a 3GPP system.

Note that, in the description herein, reference may be made to the term“cell;” however, particularly with respect to 5G NR concepts, beams maybe used instead of cells and, as such, it is important to note that theconcepts described herein are equally applicable to both cells andbeams.

Particular embodiments include parity check (PC) bit generation forPolar codes. The embodiments may be classified into at least two groupsof embodiments. A first group of embodiments includes cumulativesummation, and a second group includes systematic coding of leastreliable data bits.

In the first group of embodiments based on cumulative summation, in aparticular embodiment each PC bit is equal to the sum of all previousbits in a non-recursive manner. That is, simple summation of all theinformation and frozen bits, excluding any previous PC bits, is used togenerate the value of each particular PC bit.

Specifically, let u=[u₀, u₁, . . . , u_(N-1)] represent the input vectorof bits to the Polar encoder core, where N is the size of the Polarcode, and let P denote the set of predetermined positions of PC bits.Then for each i∈P, the value of the corresponding PC bit can be computedsimply by

u _(i)=Σ_(j∈{0,1, . . . ,N-1}\P:j≤i) u _(j).

In other words, the value of each PC bit is the binary sum (i.e., XOR)of all bit values in front of it, except those values of other PC bits.

In another embodiment, each PC bit is equal to the sum of all previousbits in a recursive manner. That is, simple summation of all theinformation and frozen bits, including any previous PC bits, is used togenerate the value of each particular PC bit. This can be achieved byshift register with feedback.

Specifically, let P={i₀, i₁, . . . , i_(|P|)} sorted in such a way thati_(m)≤i_(n) whenever m≤n. Incrementing m sequentially from 0 to |P| (thenumber of elements in P), the value of the m-th PC bit can be computedsimply by

u _(i) _(m) =Σ_(j∈{0,1, . . . ,N-1}:j≤i) _(m) u _(j).

In other words, the value of each PC bit is the binary sum (i.e. XOR) ofall bit values in front of it, including those values of otherpreviously computed PC bits.

In a second group of embodiments based on systematic coding of leastreliable data bits, in a particular embodiment the PC bits are generatedbased on a systematic block code on the least reliable data bits.Specifically, let Λ⊂{0, 1, . . . , N−1} denote the K_(PC) least reliablebit positions among the K bit positions that are chosen to carry databits, where |Λ|=K_(PC) and K_(PC)≤K. Also let Φ denote a K_(PC) byn_(PC) parity check matrix so that G=[I,Φ] forms the generator matrix ofa (K_(PC), K_(PC)+n_(PC)) systematic code with a good minimum-distanceproperty, where I denotes an K_(PC) by K_(PC) identity matrix. LetP={i₀, i₁, . . . , i_(|P|-1)} be the position indices of the PC bits.Then for each i∈P, the value of the m-th PC bit, where m=0, 1, . . . ,|P|−1, and without loss of generality, |P|=n_(PC) is computed as

u _(i) _(m) =u _(R)·[Φ]_(m)

where [Φ]_(m) denotes the m-th column of Φ, and u_(R) denotes a rowvector formed by the elements in the set {u_(j):j∈Λ} with indices sortedin ascending order. The vector u_(R) contains the data bits that arecarried by the K_(PC) least reliable positions.

According to one aspect of this embodiment, the size of the set A (i.e.,K_(PC)) is selected based on the code rate R=(K+n_(PC))/M, where Mdenotes the code length after rate-matching operations. In general,K_(PC) and n_(PC) are selected so that K_(PC)/(K_(PC)+n_(PC)) iscomparable to, or slightly below, the code rate R. That is, choosing(K_(PC),n_(PC)) such that

$\frac{K_{PC}}{K_{PC} + n_{PC}} \leq \frac{K + n_{PC}}{M}$

which provides a guideline for choosing K_(PC) for a given n_(PC).

FIG. 4 illustrates an encoder with a cyclic redundancy check attachment,according to various embodiments. Meanwhile, FIG. 5 illustrates amodified successive cancellation list (SCL) Polar decoder anddeinterleaver. Embodiments disclosed herein could, for example, beimplemented within environments utilizing such Polar encoding/decodingfunctionalities.

Although the subject matter described herein may be implemented in anyappropriate type of system using any suitable components, theembodiments disclosed herein are described in relation to a wirelessnetwork, such as the example wireless network illustrated in FIG. 6. Forsimplicity, the wireless network of FIG. 6 only depicts network 106,network nodes 160 and 160 b, and WDs 110, 110 b, and 110 c. In practice,a wireless network may further include any additional elements suitableto support communication between wireless devices or between a wirelessdevice and another communication device, such as a landline telephone, aservice provider, or any other network node or end device. Of theillustrated components, network node 160 and wireless device (WD) 110are depicted with additional detail. The wireless network may providecommunication and other types of services to one or more wirelessdevices to facilitate the wireless devices' access to and/or use of theservices provided by, or via, the wireless network.

The wireless network may comprise and/or interface with any type ofcommunication, telecommunication, data, cellular, and/or radio networkor other similar type of system. In some embodiments, the wirelessnetwork may be configured to operate according to specific standards orother types of predefined rules or procedures. Thus, particularembodiments of the wireless network may implement communicationstandards, such as Global System for Mobile Communications (GSM),Universal Mobile Telecommunications System (UMTS), Long Term Evolution(LTE), and/or other suitable 2G, 3G, 4G, or 5G standards; wireless localarea network (WLAN) standards, such as the IEEE 802.11 standards; and/orany other appropriate wireless communication standard, such as theWorldwide Interoperability for Microwave Access (WiMax), Bluetooth,Z-Wave and/or ZigBee standards.

Network 106 may comprise one or more backhaul networks, core networks,IP networks, public switched telephone networks (PSTNs), packet datanetworks, optical networks, wide-area networks (WANs), local areanetworks (LANs), wireless local area networks (WLANs), wired networks,wireless networks, metropolitan area networks, and other networks toenable communication between devices.

Network node 160 and WD 110 comprise various components described inmore detail below. These components work together in order to providenetwork node and/or wireless device functionality, such as providingwireless connections in a wireless network. In different embodiments,the wireless network may comprise any number of wired or wirelessnetworks, network nodes, base stations, controllers, wireless devices,relay stations, and/or any other components or systems that mayfacilitate or participate in the communication of data and/or signalswhether via wired or wireless connections.

As used herein, network node refers to equipment capable, configured,arranged and/or operable to communicate directly or indirectly with awireless device and/or with other network nodes or equipment in thewireless network to enable and/or provide wireless access to thewireless device and/or to perform other functions (e.g., administration)in the wireless network. Examples of network nodes include, but are notlimited to, access points (APs) (e.g., radio access points), basestations (BSs) (e.g., radio base stations, Node Bs, evolved Node Bs(eNBs) and NR NodeBs (gNBs)). Base stations may be categorized based onthe amount of coverage they provide (or, stated differently, theirtransmit power level) and may then also be referred to as femto basestations, pico base stations, micro base stations, or macro basestations. A base station may be a relay node or a relay donor nodecontrolling a relay. A network node may also include one or more (orall) parts of a distributed radio base station such as centralizeddigital units and/or remote radio units (RRUs), sometimes referred to asRemote Radio Heads (RRHs). Such remote radio units may or may not beintegrated with an antenna as an antenna integrated radio. Parts of adistributed radio base station may also be referred to as nodes in adistributed antenna system (DAS). Yet further examples of network nodesinclude multi-standard radio (MSR) equipment such as MSR BSs, networkcontrollers such as radio network controllers (RNCs) or base stationcontrollers (BSCs), base transceiver stations (BTSs), transmissionpoints, transmission nodes, multi-cell/multicast coordination entities(MCEs), core network nodes (e.g., MSCs, MMEs), O&M nodes, OSS nodes, SONnodes, positioning nodes (e.g., E-SMLCs), and/or MDTs. As anotherexample, a network node may be a virtual network node as described inmore detail below. More generally, however, network nodes may representany suitable device (or group of devices) capable, configured, arranged,and/or operable to enable and/or provide a wireless device with accessto the wireless network or to provide some service to a wireless devicethat has accessed the wireless network.

In FIG. 6, network node 160 includes processing circuitry 170, devicereadable medium 180, interface 190, auxiliary equipment 184, powersource 186, power circuitry 187, and antenna 162. Although network node160 illustrated in the example wireless network of FIG. 6 may representa device that includes the illustrated combination of hardwarecomponents, other embodiments may comprise network nodes with differentcombinations of components. It is to be understood that a network nodecomprises any suitable combination of hardware and/or software needed toperform the tasks, features, functions and methods disclosed herein.Moreover, while the components of network node 160 are depicted assingle boxes located within a larger box, or nested within multipleboxes, in practice, a network node may comprise multiple differentphysical components that make up a single illustrated component (e.g.,device readable medium 180 may comprise multiple separate hard drives aswell as multiple RAM modules).

Similarly, network node 160 may be composed of multiple physicallyseparate components (e.g., a NodeB component and a RNC component, or aBTS component and a BSC component, etc.), which may each have their ownrespective components. In certain scenarios in which network node 160comprises multiple separate components (e.g., BTS and BSC components),one or more of the separate components may be shared among severalnetwork nodes. For example, a single RNC may control multiple NodeB's.In such a scenario, each unique NodeB and RNC pair, may in someinstances be considered a single separate network node. In someembodiments, network node 160 may be configured to support multipleradio access technologies (RATs). In such embodiments, some componentsmay be duplicated (e.g., separate device readable medium 180 for thedifferent RATs) and some components may be reused (e.g., the sameantenna 162 may be shared by the RATs). Network node 160 may alsoinclude multiple sets of the various illustrated components fordifferent wireless technologies integrated into network node 160, suchas, for example, GSM, WCDMA, LTE, NR, WiFi, or Bluetooth wirelesstechnologies. These wireless technologies may be integrated into thesame or different chip or set of chips and other components withinnetwork node 160.

Processing circuitry 170 is configured to perform any determining,calculating, or similar operations (e.g., certain obtaining operations)described herein as being provided by a network node. These operationsperformed by processing circuitry 170 may include processing informationobtained by processing circuitry 170 by, for example, converting theobtained information into other information, comparing the obtainedinformation or converted information to information stored in thenetwork node, and/or performing one or more operations based on theobtained information or converted information, and as a result of saidprocessing making a determination.

Processing circuitry 170 may comprise a combination of one or more of amicroprocessor, controller, microcontroller, central processing unit,digital signal processor, application-specific integrated circuit, fieldprogrammable gate array, or any other suitable computing device,resource, or combination of hardware, software and/or encoded logicoperable to provide, either alone or in conjunction with other networknode 160 components, such as device readable medium 180, network node160 functionality. For example, processing circuitry 170 may executeinstructions stored in device readable medium 180 or in memory withinprocessing circuitry 170. Such functionality may include providing anyof the various wireless features, functions, or benefits discussedherein. In some embodiments, processing circuitry 170 may include asystem on a chip (SOC).

In some embodiments, processing circuitry 170 may include one or more ofradio frequency (RF) transceiver circuitry 172 and baseband processingcircuitry 174. In some embodiments, radio frequency (RF) transceivercircuitry 172 and baseband processing circuitry 174 may be on separatechips (or sets of chips), boards, or units, such as radio units anddigital units. In alternative embodiments, part or all of RF transceivercircuitry 172 and baseband processing circuitry 174 may be on the samechip or set of chips, boards, or units

In certain embodiments, some or all of the functionality describedherein as being provided by a network node, base station, eNB or othersuch network device may be performed by processing circuitry 170executing instructions stored on device readable medium 180 or memorywithin processing circuitry 170. In alternative embodiments, some or allof the functionality may be provided by processing circuitry 170 withoutexecuting instructions stored on a separate or discrete device readablemedium, such as in a hard-wired manner. In any of those embodiments,whether executing instructions stored on a device readable storagemedium or not, processing circuitry 170 can be configured to perform thedescribed functionality. The benefits provided by such functionality arenot limited to processing circuitry 170 alone or to other components ofnetwork node 160, but are enjoyed by network node 160 as a whole, and/orby end users and the wireless network generally.

Device readable medium 180 may comprise any form of volatile ornon-volatile computer readable memory including, without limitation,persistent storage, solid-state memory, remotely mounted memory,magnetic media, optical media, random access memory (RAM), read-onlymemory (ROM), mass storage media (for example, a hard disk), removablestorage media (for example, a flash drive, a Compact Disk (CD) or aDigital Video Disk (DVD)), and/or any other volatile or non-volatile,non-transitory device readable and/or computer-executable memory devicesthat store information, data, and/or instructions that may be used byprocessing circuitry 170. Device readable medium 180 may store anysuitable instructions, data or information, including a computerprogram, software, an application including one or more of logic, rules,code, tables, etc. and/or other instructions capable of being executedby processing circuitry 170 and, utilized by network node 160. Devicereadable medium 180 may be used to store any calculations made byprocessing circuitry 170 and/or any data received via interface 190. Insome embodiments, processing circuitry 170 and device readable medium180 may be considered to be integrated.

Interface 190 is used in the wired or wireless communication ofsignalling and/or data between network node 160, network 106, and/or WDs110. As illustrated, interface 190 comprises port(s)/terminal(s) 194 tosend and receive data, for example to and from network 106 over a wiredconnection. Interface 190 also includes radio front end circuitry 192that may be coupled to, or in certain embodiments a part of, antenna162. Radio front end circuitry 192 comprises filters 198 and amplifiers196. Radio front end circuitry 192 may be connected to antenna 162 andprocessing circuitry 170. Radio front end circuitry may be configured tocondition signals communicated between antenna 162 and processingcircuitry 170. Radio front end circuitry 192 may receive digital datathat is to be sent out to other network nodes or WDs via a wirelessconnection. Radio front end circuitry 192 may convert the digital datainto a radio signal having the appropriate channel and bandwidthparameters using a combination of filters 198 and/or amplifiers 196. Theradio signal may then be transmitted via antenna 162. Similarly, whenreceiving data, antenna 162 may collect radio signals which are thenconverted into digital data by radio front end circuitry 192. Thedigital data may be passed to processing circuitry 170. In otherembodiments, the interface may comprise different components and/ordifferent combinations of components.

In certain alternative embodiments, network node 160 may not includeseparate radio front end circuitry 192, instead, processing circuitry170 may comprise radio front end circuitry and may be connected toantenna 162 without separate radio front end circuitry 192. Similarly,in some embodiments, all or some of RF transceiver circuitry 172 may beconsidered a part of interface 190. In still other embodiments,interface 190 may include one or more ports or terminals 194, radiofront end circuitry 192, and RF transceiver circuitry 172, as part of aradio unit (not shown), and interface 190 may communicate with basebandprocessing circuitry 174, which is part of a digital unit (not shown).

Antenna 162 may include one or more antennas, or antenna arrays,configured to send and/or receive wireless signals. Antenna 162 may becoupled to radio front end circuitry 190 and may be any type of antennacapable of transmitting and receiving data and/or signals wirelessly. Insome embodiments, antenna 162 may comprise one or more omni-directional,sector or panel antennas operable to transmit/receive radio signalsbetween, for example, 2 GHz and 66 GHz. An omni-directional antenna maybe used to transmit/receive radio signals in any direction, a sectorantenna may be used to transmit/receive radio signals from deviceswithin a particular area, and a panel antenna may be a line of sightantenna used to transmit/receive radio signals in a relatively straightline. In some instances, the use of more than one antenna may bereferred to as MIMO. In certain embodiments, antenna 162 may be separatefrom network node 160 and may be connectable to network node 160 throughan interface or port.

Antenna 162, interface 190, and/or processing circuitry 170 may beconfigured to perform any receiving operations and/or certain obtainingoperations described herein as being performed by a network node. Anyinformation, data and/or signals may be received from a wireless device,another network node and/or any other network equipment. Similarly,antenna 162, interface 190, and/or processing circuitry 170 may beconfigured to perform any transmitting operations described herein asbeing performed by a network node. Any information, data and/or signalsmay be transmitted to a wireless device, another network node and/or anyother network equipment.

Power circuitry 187 may comprise, or be coupled to, power managementcircuitry and is configured to supply the components of network node 160with power for performing the functionality described herein. Powercircuitry 187 may receive power from power source 186. Power source 186and/or power circuitry 187 may be configured to provide power to thevarious components of network node 160 in a form suitable for therespective components (e.g., at a voltage and current level needed foreach respective component). Power source 186 may either be included in,or external to, power circuitry 187 and/or network node 160. Forexample, network node 160 may be connectable to an external power source(e.g., an electricity outlet) via an input circuitry or interface suchas an electrical cable, whereby the external power source supplies powerto power circuitry 187. As a further example, power source 186 maycomprise a source of power in the form of a battery or battery packwhich is connected to, or integrated in, power circuitry 187. Thebattery may provide backup power should the external power source fail.Other types of power sources, such as photovoltaic devices, may also beused.

Alternative embodiments of network node 160 may include additionalcomponents beyond those shown in FIG. 6 that may be responsible forproviding certain aspects of the network node's functionality, includingany of the functionality described herein and/or any functionalitynecessary to support the subject matter described herein. For example,network node 160 may include user interface equipment to allow input ofinformation into network node 160 and to allow output of informationfrom network node 160. This may allow a user to perform diagnostic,maintenance, repair, and other administrative functions for network node160.

As used herein, wireless device (WD) refers to a device capable,configured, arranged and/or operable to communicate wirelessly withnetwork nodes and/or other wireless devices. Unless otherwise noted, theterm WD may be used interchangeably herein with user equipment (UE).Communicating wirelessly may involve transmitting and/or receivingwireless signals using electromagnetic waves, radio waves, infraredwaves, and/or other types of signals suitable for conveying informationthrough air. In some embodiments, a WD may be configured to transmitand/or receive information without direct human interaction. Forinstance, a WD may be designed to transmit information to a network on apredetermined schedule, when triggered by an internal or external event,or in response to requests from the network. Examples of a WD include,but are not limited to, a smart phone, a mobile phone, a cell phone, avoice over IP (VoIP) phone, a wireless local loop phone, a desktopcomputer, a personal digital assistant (PDA), a wireless cameras, agaming console or device, a music storage device, a playback appliance,a wearable terminal device, a wireless endpoint, a mobile station, atablet, a laptop, a laptop-embedded equipment (LEE), a laptop-mountedequipment (LME), a smart device, a wireless customer-premise equipment(CPE). a vehicle-mounted wireless terminal device, etc. A WD may supportdevice-to-device (D2D) communication, for example by implementing a 3GPPstandard for sidelink communication, vehicle-to-vehicle (V2V),vehicle-to-infrastructure (V2I), vehicle-to-everything (V2X) and may inthis case be referred to as a D2D communication device. As yet anotherspecific example, in an Internet of Things (IoT) scenario, a WD mayrepresent a machine or other device that performs monitoring and/ormeasurements, and transmits the results of such monitoring and/ormeasurements to another WD and/or a network node. The WD may in thiscase be a machine-to-machine (M2M) device, which may in a 3GPP contextbe referred to as an MTC device. As one particular example, the WD maybe a UE implementing the 3GPP narrow band internet of things (NB-IoT)standard. Particular examples of such machines or devices are sensors,metering devices such as power meters, industrial machinery, or home orpersonal appliances (e.g. refrigerators, televisions, etc.) personalwearables (e.g., watches, fitness trackers, etc.). In other scenarios, aWD may represent a vehicle or other equipment that is capable ofmonitoring and/or reporting on its operational status or other functionsassociated with its operation. A WD as described above may represent theendpoint of a wireless connection, in which case the device may bereferred to as a wireless terminal. Furthermore, a WD as described abovemay be mobile, in which case it may also be referred to as a mobiledevice or a mobile terminal.

As illustrated, wireless device 110 includes antenna 111, interface 114,processing circuitry 120, device readable medium 130, user interfaceequipment 132, auxiliary equipment 134, power source 136 and powercircuitry 137. WD 110 may include multiple sets of one or more of theillustrated components for different wireless technologies supported byWD 110, such as, for example, GSM, WCDMA, LTE, NR, WiFi, WiMAX, orBluetooth wireless technologies, just to mention a few. These wirelesstechnologies may be integrated into the same or different chips or setof chips as other components within WD 110.

Antenna 111 may include one or more antennas or antenna arrays,configured to send and/or receive wireless signals, and is connected tointerface 114. In certain alternative embodiments, antenna 111 may beseparate from WD 110 and be connectable to WD 110 through an interfaceor port. Antenna 111, interface 114, and/or processing circuitry 120 maybe configured to perform any receiving or transmitting operationsdescribed herein as being performed by a WD. Any information, dataand/or signals may be received from a network node and/or another WD. Insome embodiments, radio front end circuitry and/or antenna 111 may beconsidered an interface.

As illustrated, interface 114 comprises radio front end circuitry 112and antenna 111. Radio front end circuitry 112 comprise one or morefilters 118 and amplifiers 116. Radio front end circuitry 114 isconnected to antenna 111 and processing circuitry 120, and is configuredto condition signals communicated between antenna 111 and processingcircuitry 120. Radio front end circuitry 112 may be coupled to or a partof antenna 111. In some embodiments, WD 110 may not include separateradio front end circuitry 112; rather, processing circuitry 120 maycomprise radio front end circuitry and may be connected to antenna 111.Similarly, in some embodiments, some or all of RF transceiver circuitry122 may be considered a part of interface 114. Radio front end circuitry112 may receive digital data that is to be sent out to other networknodes or WDs via a wireless connection. Radio front end circuitry 112may convert the digital data into a radio signal having the appropriatechannel and bandwidth parameters using a combination of filters 118and/or amplifiers 116. The radio signal may then be transmitted viaantenna 111. Similarly, when receiving data, antenna 111 may collectradio signals which are then converted into digital data by radio frontend circuitry 112. The digital data may be passed to processingcircuitry 120. In other embodiments, the interface may comprisedifferent components and/or different combinations of components.

Processing circuitry 120 may comprise a combination of one or more of amicroprocessor, controller, microcontroller, central processing unit,digital signal processor, application-specific integrated circuit, fieldprogrammable gate array, or any other suitable computing device,resource, or combination of hardware, software, and/or encoded logicoperable to provide, either alone or in conjunction with other WD 110components, such as device readable medium 130, WD 110 functionality.Such functionality may include providing any of the various wirelessfeatures or benefits discussed herein. For example, processing circuitry120 may execute instructions stored in device readable medium 130 or inmemory within processing circuitry 120 to provide the functionalitydisclosed herein.

As illustrated, processing circuitry 120 includes one or more of RFtransceiver circuitry 122, baseband processing circuitry 124, andapplication processing circuitry 126. In other embodiments, theprocessing circuitry may comprise different components and/or differentcombinations of components. In certain embodiments processing circuitry120 of WD 110 may comprise a SOC. In some embodiments, RF transceivercircuitry 122, baseband processing circuitry 124, and applicationprocessing circuitry 126 may be on separate chips or sets of chips. Inalternative embodiments, part or all of baseband processing circuitry124 and application processing circuitry 126 may be combined into onechip or set of chips, and RF transceiver circuitry 122 may be on aseparate chip or set of chips. In still alternative embodiments, part orall of RF transceiver circuitry 122 and baseband processing circuitry124 may be on the same chip or set of chips, and application processingcircuitry 126 may be on a separate chip or set of chips. In yet otheralternative embodiments, part or all of RF transceiver circuitry 122,baseband processing circuitry 124, and application processing circuitry126 may be combined in the same chip or set of chips. In someembodiments, RF transceiver circuitry 122 may be a part of interface114. RF transceiver circuitry 122 may condition RF signals forprocessing circuitry 120.

In certain embodiments, some or all of the functionality describedherein as being performed by a WD may be provided by processingcircuitry 120 executing instructions stored on device readable medium130, which in certain embodiments may be a computer-readable storagemedium. In alternative embodiments, some or all of the functionality maybe provided by processing circuitry 120 without executing instructionsstored on a separate or discrete device readable storage medium, such asin a hard-wired manner. In any of those particular embodiments, whetherexecuting instructions stored on a device readable storage medium ornot, processing circuitry 120 can be configured to perform the describedfunctionality. The benefits provided by such functionality are notlimited to processing circuitry 120 alone or to other components of WD110, but are enjoyed by WD 110 as a whole, and/or by end users and thewireless network generally.

Processing circuitry 120 may be configured to perform any determining,calculating, or similar operations (e.g., certain obtaining operations)described herein as being performed by a WD. These operations, asperformed by processing circuitry 120, may include processinginformation obtained by processing circuitry 120 by, for example,converting the obtained information into other information, comparingthe obtained information or converted information to information storedby WD 110, and/or performing one or more operations based on theobtained information or converted information, and as a result of saidprocessing making a determination.

Device readable medium 130 may be operable to store a computer program,software, an application including one or more of logic, rules, code,tables, etc. and/or other instructions capable of being executed byprocessing circuitry 120. Device readable medium 130 may includecomputer memory (e.g., Random Access Memory (RAM) or Read Only Memory(ROM)), mass storage media (e.g., a hard disk), removable storage media(e.g., a Compact Disk (CD) or a Digital Video Disk (DVD)), and/or anyother volatile or non-volatile, non-transitory device readable and/orcomputer executable memory devices that store information, data, and/orinstructions that may be used by processing circuitry 120. In someembodiments, processing circuitry 120 and device readable medium 130 maybe considered to be integrated.

User interface equipment 132 may provide components that allow for ahuman user to interact with WD 110. Such interaction may be of manyforms, such as visual, audial, tactile, etc. User interface equipment132 may be operable to produce output to the user and to allow the userto provide input to WD 110. The type of interaction may vary dependingon the type of user interface equipment 132 installed in WD 110. Forexample, if WD 110 is a smart phone, the interaction may be via a touchscreen; if WD 110 is a smart meter, the interaction may be through ascreen that provides usage (e.g., the number of gallons used) or aspeaker that provides an audible alert (e.g., if smoke is detected).User interface equipment 132 may include input interfaces, devices andcircuits, and output interfaces, devices and circuits. User interfaceequipment 132 is configured to allow input of information into WD 110,and is connected to processing circuitry 120 to allow processingcircuitry 120 to process the input information. User interface equipment132 may include, for example, a microphone, a proximity or other sensor,keys/buttons, a touch display, one or more cameras, a USB port, or otherinput circuitry. User interface equipment 132 is also configured toallow output of information from WD 110, and to allow processingcircuitry 120 to output information from WD 110. User interfaceequipment 132 may include, for example, a speaker, a display, vibratingcircuitry, a USB port, a headphone interface, or other output circuitry.Using one or more input and output interfaces, devices, and circuits, ofuser interface equipment 132, WD 110 may communicate with end usersand/or the wireless network, and allow them to benefit from thefunctionality described herein.

Auxiliary equipment 134 is operable to provide more specificfunctionality which may not be generally performed by WDs. This maycomprise specialized sensors for doing measurements for variouspurposes, interfaces for additional types of communication such as wiredcommunications etc. The inclusion and type of components of auxiliaryequipment 134 may vary depending on the embodiment and/or scenario.

Power source 136 may, in some embodiments, be in the form of a batteryor battery pack. Other types of power sources, such as an external powersource (e.g., an electricity outlet), photovoltaic devices or powercells, may also be used. WD 110 may further comprise power circuitry 137for delivering power from power source 136 to the various parts of WD110 which need power from power source 136 to carry out anyfunctionality described or indicated herein. Power circuitry 137 may incertain embodiments comprise power management circuitry. Power circuitry137 may additionally or alternatively be operable to receive power froman external power source; in which case WD 110 may be connectable to theexternal power source (such as an electricity outlet) via inputcircuitry or an interface such as an electrical power cable. Powercircuitry 137 may also in certain embodiments be operable to deliverpower from an external power source to power source 136. This may be,for example, for the charging of power source 136. Power circuitry 137may perform any formatting, converting, or other modification to thepower from power source 136 to make the power suitable for therespective components of WD 110 to which power is supplied.

FIG. 7 illustrates one embodiment of a UE in accordance with variousaspects described herein. As used herein, a user equipment or UE may notnecessarily have a user in the sense of a human user who owns and/oroperates the relevant device. Instead, a UE may represent a device thatis intended for sale to, or operation by, a human user but which maynot, or which may not initially, be associated with a specific humanuser (e.g., a smart sprinkler controller). Alternatively, a UE mayrepresent a device that is not intended for sale to, or operation by, anend user but which may be associated with or operated for the benefit ofa user (e.g., a smart power meter). UE 2200 may be any UE identified bythe 3^(rd) Generation Partnership Project (3GPP), including a NB-IoT UE,a machine type communication (MTC) UE, and/or an enhanced MTC (eMTC) UE.UE 200, as illustrated in FIG. 7, is one example of a WD configured forcommunication in accordance with one or more communication standardspromulgated by the 3^(rd) Generation Partnership Project (3GPP), such as3GPP's GSM, UMTS, LTE, and/or 5G standards. As mentioned previously, theterm WD and UE may be used interchangeable. Accordingly, although FIG. 7is a UE, the components discussed herein are equally applicable to a WD,and vice-versa.

In FIG. 7, UE 200 includes processing circuitry 201 that is operativelycoupled to input/output interface 205, radio frequency (RF) interface209, network connection interface 211, memory 215 including randomaccess memory (RAM) 217, read-only memory (ROM) 219, and storage medium221 or the like, communication subsystem 231, power source 233, and/orany other component, or any combination thereof. Storage medium 221includes operating system 223, application program 225, and data 227. Inother embodiments, storage medium 221 may include other similar types ofinformation. Certain UEs may utilize all of the components shown in FIG.7, or only a subset of the components. The level of integration betweenthe components may vary from one UE to another UE. Further, certain UEsmay contain multiple instances of a component, such as multipleprocessors, memories, transceivers, transmitters, receivers, etc.

In FIG. 7, processing circuitry 201 may be configured to processcomputer instructions and data. Processing circuitry 201 may beconfigured to implement any sequential state machine operative toexecute machine instructions stored as machine-readable computerprograms in the memory, such as one or more hardware-implemented statemachines (e.g., in discrete logic, FPGA, ASIC, etc.); programmable logictogether with appropriate firmware; one or more stored program,general-purpose processors, such as a microprocessor or Digital SignalProcessor (DSP), together with appropriate software; or any combinationof the above. For example, the processing circuitry 201 may include twocentral processing units (CPUs). Data may be information in a formsuitable for use by a computer.

In the depicted embodiment, input/output interface 205 may be configuredto provide a communication interface to an input device, output device,or input and output device. UE 200 may be configured to use an outputdevice via input/output interface 205. An output device may use the sametype of interface port as an input device. For example, a USB port maybe used to provide input to and output from UE 200. The output devicemay be a speaker, a sound card, a video card, a display, a monitor, aprinter, an actuator, an emitter, a smartcard, another output device, orany combination thereof. UE 200 may be configured to use an input devicevia input/output interface 205 to allow a user to capture informationinto UE 200. The input device may include a touch-sensitive orpresence-sensitive display, a camera (e.g., a digital camera, a digitalvideo camera, a web camera, etc.), a microphone, a sensor, a mouse, atrackball, a directional pad, a trackpad, a scroll wheel, a smartcard,and the like. The presence-sensitive display may include a capacitive orresistive touch sensor to sense input from a user. A sensor may be, forinstance, an accelerometer, a gyroscope, a tilt sensor, a force sensor,a magnetometer, an optical sensor, a proximity sensor, another likesensor, or any combination thereof. For example, the input device may bean accelerometer, a magnetometer, a digital camera, a microphone, and anoptical sensor.

In FIG. 7, RF interface 209 may be configured to provide a communicationinterface to RF components such as a transmitter, a receiver, and anantenna. Network connection interface 211 may be configured to provide acommunication interface to network 243 a. Network 243 a may encompasswired and/or wireless networks such as a local-area network (LAN), awide-area network (WAN), a computer network, a wireless network, atelecommunications network, another like network or any combinationthereof. For example, network 243 a may comprise a Wi-Fi network.Network connection interface 211 may be configured to include a receiverand a transmitter interface used to communicate with one or more otherdevices over a communication network according to one or morecommunication protocols, such as Ethernet, TCP/IP, SONET, ATM, or thelike. Network connection interface 211 may implement receiver andtransmitter functionality appropriate to the communication network links(e.g., optical, electrical, and the like). The transmitter and receiverfunctions may share circuit components, software or firmware, oralternatively may be implemented separately.

RAM 217 may be configured to interface via bus 202 to processingcircuitry 201 to provide storage or caching of data or computerinstructions during the execution of software programs such as theoperating system, application programs, and device drivers. ROM 219 maybe configured to provide computer instructions or data to processingcircuitry 201. For example, ROM 219 may be configured to store invariantlow-level system code or data for basic system functions such as basicinput and output (I/O), startup, or reception of keystrokes from akeyboard that are stored in a non-volatile memory. Storage medium 221may be configured to include memory such as RAM, ROM, programmableread-only memory (PROM), erasable programmable read-only memory (EPROM),electrically erasable programmable read-only memory (EEPROM), magneticdisks, optical disks, floppy disks, hard disks, removable cartridges, orflash drives. In one example, storage medium 221 may be configured toinclude operating system 223, application program 225 such as a webbrowser application, a widget or gadget engine or another application,and data file 227. Storage medium 221 may store, for use by UE 200, anyof a variety of various operating systems or combinations of operatingsystems.

Storage medium 221 may be configured to include a number of physicaldrive units, such as redundant array of independent disks (RAID), floppydisk drive, flash memory, USB flash drive, external hard disk drive,thumb drive, pen drive, key drive, high-density digital versatile disc(HD-DVD) optical disc drive, internal hard disk drive, Blu-Ray opticaldisc drive, holographic digital data storage (HDDS) optical disc drive,external mini-dual in-line memory module (DIMM), synchronous dynamicrandom access memory (SDRAM), external micro-DIMM SDRAM, smartcardmemory such as a subscriber identity module or a removable user identity(SIM/RUIM) module, other memory, or any combination thereof. Storagemedium 221 may allow UE 200 to access computer-executable instructions,application programs or the like, stored on transitory or non-transitorymemory media, to off-load data, or to upload data. An article ofmanufacture, such as one utilizing a communication system may betangibly embodied in storage medium 221, which may comprise a devicereadable medium.

In FIG. 7, processing circuitry 201 may be configured to communicatewith network 243 b using communication subsystem 231. Network 243 a andnetwork 243 b may be the same network or networks or different networkor networks. Communication subsystem 231 may be configured to includeone or more transceivers used to communicate with network 243 b. Forexample, communication subsystem 231 may be configured to include one ormore transceivers used to communicate with one or more remotetransceivers of another device capable of wireless communication such asanother WD, UE, or base station of a radio access network (RAN)according to one or more communication protocols, such as IEEE 802.2,CDMA, WCDMA, GSM, LTE, UTRAN, WiMax, or the like. Each transceiver mayinclude transmitter 233 and/or receiver 235 to implement transmitter orreceiver functionality, respectively, appropriate to the RAN links(e.g., frequency allocations and the like). Further, transmitter 233 andreceiver 235 of each transceiver may share circuit components, softwareor firmware, or alternatively may be implemented separately.

In the illustrated embodiment, the communication functions ofcommunication subsystem 231 may include data communication, voicecommunication, multimedia communication, short-range communications suchas Bluetooth, near-field communication, location-based communicationsuch as the use of the global positioning system (GPS) to determine alocation, another like communication function, or any combinationthereof. For example, communication subsystem 231 may include cellularcommunication, Wi-Fi communication, Bluetooth communication, and GPScommunication. Network 243 b may encompass wired and/or wirelessnetworks such as a local-area network (LAN), a wide-area network (WAN),a computer network, a wireless network, a telecommunications network,another like network or any combination thereof. For example, network243 b may be a cellular network, a Wi-Fi network, and/or a near-fieldnetwork. Power source 213 may be configured to provide alternatingcurrent (AC) or direct current (DC) power to components of UE 200.

The features, benefits and/or functions described herein may beimplemented in one of the components of UE 200 or partitioned acrossmultiple components of UE 200. Further, the features, benefits, and/orfunctions described herein may be implemented in any combination ofhardware, software or firmware. In one example, communication subsystem231 may be configured to include any of the components described herein.Further, processing circuitry 201 may be configured to communicate withany of such components over bus 202. In another example, any of suchcomponents may be represented by program instructions stored in memorythat when executed by processing circuitry 201 perform the correspondingfunctions described herein. In another example, the functionality of anyof such components may be partitioned between processing circuitry 201and communication subsystem 231. In another example, thenon-computationally intensive functions of any of such components may beimplemented in software or firmware and the computationally intensivefunctions may be implemented in hardware.

FIG. 8 is a schematic block diagram illustrating a virtualizationenvironment 300 in which functions implemented by some embodiments maybe virtualized. In the present context, virtualizing means creatingvirtual versions of apparatuses or devices which may includevirtualizing hardware platforms, storage devices and networkingresources. As used herein, virtualization can be applied to a node(e.g., a virtualized base station or a virtualized radio access node) orto a device (e.g., a UE, a wireless device or any other type ofcommunication device) or components thereof and relates to animplementation in which at least a portion of the functionality isimplemented as one or more virtual components (e.g., via one or moreapplications, components, functions, virtual machines or containersexecuting on one or more physical processing nodes in one or morenetworks).

In some embodiments, some or all of the functions described herein maybe implemented as virtual components executed by one or more virtualmachines implemented in one or more virtual environments 300 hosted byone or more of hardware nodes 330. Further, in embodiments in which thevirtual node is not a radio access node or does not require radioconnectivity (e.g., a core network node), then the network node may beentirely virtualized.

The functions may be implemented by one or more applications 320 (whichmay alternatively be called software instances, virtual appliances,network functions, virtual nodes, virtual network functions, etc.)operative to implement some of the features, functions, and/or benefitsof some of the embodiments disclosed herein. Applications 320 are run invirtualization environment 300 which provides hardware 330 comprisingprocessing circuitry 360 and memory 390. Memory 390 containsinstructions 395 executable by processing circuitry 360 wherebyapplication 320 is operative to provide one or more of the features,benefits, and/or functions disclosed herein.

Virtualization environment 300, comprises general-purpose orspecial-purpose network hardware devices 330 comprising a set of one ormore processors or processing circuitry 360, which may be commercialoff-the-shelf (COTS) processors, dedicated Application SpecificIntegrated Circuits (ASICs), or any other type of processing circuitryincluding digital or analog hardware components or special purposeprocessors. Each hardware device may comprise memory 390-1 which may benon-persistent memory for temporarily storing instructions 395 orsoftware executed by processing circuitry 360. Each hardware device maycomprise one or more network interface controllers (NICs) 370, alsoknown as network interface cards, which include physical networkinterface 380. Each hardware device may also include non-transitory,persistent, machine-readable storage media 390-2 having stored thereinsoftware 395 and/or instructions executable by processing circuitry 360.Software 395 may include any type of software including software forinstantiating one or more virtualization layers 350 (also referred to ashypervisors), software to execute virtual machines 340 as well assoftware allowing it to execute functions, features and/or benefitsdescribed in relation with some embodiments described herein.

Virtual machines 340, comprise virtual processing, virtual memory,virtual networking or interface and virtual storage, and may be run by acorresponding virtualization layer 350 or hypervisor. Differentembodiments of the instance of virtual appliance 320 may be implementedon one or more of virtual machines 340, and the implementations may bemade in different ways.

During operation, processing circuitry 360 executes software 395 toinstantiate the hypervisor or virtualization layer 350, which maysometimes be referred to as a virtual machine monitor (VMM).Virtualization layer 350 may present a virtual operating platform thatappears like networking hardware to virtual machine 340.

As shown in FIG. 8, hardware 330 may be a standalone network node withgeneric or specific components. Hardware 330 may comprise antenna 3225and may implement some functions via virtualization. Alternatively,hardware 330 may be part of a larger cluster of hardware (e.g. such asin a data center or customer premise equipment (CPE)) where manyhardware nodes work together and are managed via management andorchestration (MANO) 3100, which, among others, oversees lifecyclemanagement of applications 320.

Virtualization of the hardware is in some contexts referred to asnetwork function virtualization (NFV). NFV may be used to consolidatemany network equipment types onto industry standard high volume serverhardware, physical switches, and physical storage, which can be locatedin data centers, and customer premise equipment.

In the context of NFV, virtual machine 340 may be a softwareimplementation of a physical machine that runs programs as if they wereexecuting on a physical, non-virtualized machine. Each of virtualmachines 340, and that part of hardware 330 that executes that virtualmachine, be it hardware dedicated to that virtual machine and/orhardware shared by that virtual machine with others of the virtualmachines 340, forms a separate virtual network elements (VNE).

Still in the context of NFV, Virtual Network Function (VNF) isresponsible for handling specific network functions that run in one ormore virtual machines 340 on top of hardware networking infrastructure330 and corresponds to application 320 in FIG. 8.

In some embodiments, one or more radio units 3200 that each include oneor more transmitters 3220 and one or more receivers 3210 may be coupledto one or more antennas 3225. Radio units 3200 may communicate directlywith hardware nodes 330 via one or more appropriate network interfacesand may be used in combination with the virtual components to provide avirtual node with radio capabilities, such as a radio access node or abase station.

In some embodiments, some signaling can be effected with the use ofcontrol system 3230 which may alternatively be used for communicationbetween the hardware nodes 330 and radio units 3200.

FIG. 9 depicts a method in accordance with particular embodiments, themethod begins at step 900 with a wireless transmitter (e.g., wirelessdevice 110, network node 160, etc.) that receives a set of informationbits. For example, network node 160 may receive a set of informationbits from a higher layer for transmission to wireless device 110.

At step 910, the wireless transmitter determines a set of parity checkbits. For example, network node 160 may determine a set of parity checkbits by, for each parity check bit in the set, determining the binarysum of all bit values in front of it. Some embodiments may include otherparity bits in the sum, while others may not include the parity bit. Inother embodiments, network node 160 may generate a set of parity checkbits based on a systematic block code on the least reliable bits of theset of information bits and frozen bits. In particular embodiments, thewireless transmitter may determine the set of parity check bitsaccording to any of the embodiments and examples described above.

At step 920, the wireless transmitter concatenates the set ofinformation bits with the set of parity check bits. For example, networknode 160 may combine the set of parity check bits with the set ofinformation bits according to any of the embodiments and examplesdescribed above.

At step 930, the wireless transmitter Polar encodes the information bitsinto a set of information bits and frozen bits. For example, networknode 160 may encode the information bits according to the Polar encodingalgorithm described above.

At step 940, the wireless transmitter transmits the encoded set of bitsto a wireless receiver. For example, network node 160 may transmit theconcatenated bits to wireless device 110.

Modifications, additions, or omissions may be made to the methodillustrated in FIG. 9. Additionally, one or more steps in method themethod of FIG. 9 may be performed in parallel or in any suitable order.

FIG. 10 depicts a method in accordance with particular embodiments, themethod begins at step 1000 with a wireless receiver (e.g., wirelessdevice 110, network node 160, etc.) that receives a set of polar codedinformation bits concatenated with a set of parity check bits. Forexample, wireless device 110 may receive a set of polar codedinformation bits concatenated with a set of parity check bits fromnetwork node 160 (e.g., as described with respect to FIG. 9).

At step 1010, the wireless receiver polar decodes the set of polar codedinformation bits concatenated with the set of parity check bits. Forexample, wireless device 110 may decode the information bits accordingto the Polar encoding algorithm described above.

At step 1020, the wireless receiver terminates the decoding when one ofthe parity check bits in the set of parity check bits indicates anerror. For example, wireless device 110 may terminate the decoding earlyonce an error is detected, according to any of the embodiments andexamples described above.

Modifications, additions, or omissions may be made to the methodillustrated in FIG. 10. Additionally, one or more steps in method themethod of FIG. 10 may be performed in parallel or in any suitable order.

FIG. 11 illustrates a schematic block diagram of an apparatus 1100 in awireless network (for example, the wireless network shown in FIG. 6).The apparatus may be implemented in a wireless device or network node(e.g., wireless device 110 or network node 160 shown in FIG. 6).Apparatus 1100 is operable to carry out the example method describedwith reference to FIG. 9 and possibly any other processes or methodsdisclosed herein. It is also to be understood that the method of FIG. 9is not necessarily carried out solely by apparatus 1100. At least someoperations of the method can be performed by one or more other entities.

Virtual Apparatus 1100 may comprise processing circuitry, which mayinclude one or more microprocessor or microcontrollers, as well as otherdigital hardware, which may include digital signal processors (DSPs),special-purpose digital logic, and the like. The processing circuitrymay be configured to execute program code stored in memory, which mayinclude one or several types of memory such as read-only memory (ROM),random-access memory, cache memory, flash memory devices, opticalstorage devices, etc. Program code stored in memory includes programinstructions for executing one or more telecommunications and/or datacommunications protocols as well as instructions for carrying out one ormore of the techniques described herein, in several embodiments. In someimplementations, the processing circuitry may be used to cause receivingunit 1110, encoding unit 1120, transmitting unit 1130, and any othersuitable units of apparatus 1100 to perform corresponding functionsaccording one or more embodiments of the present disclosure.

As illustrated in FIG. 11, apparatus 1100 includes receiving unit 1110,encoding unit 1120, and transmitting unit 1130. Receiving unit 1110 isconfigured to receive a set of information bits for encoding andtransmission. Encoding unit 1120 is configured to; determine a set ofparity check bits; and concatenate the set of information bits with theset of parity check bits; and Polar encode the information bits into aset of information bits and frozen bits. Transmitting unit 1130 isconfigured to transmit the encoded bits to a wireless receiver.

FIG. 12 illustrates a schematic block diagram of an apparatus 1200 in awireless network (for example, the wireless network shown in FIG. 6).The apparatus may be implemented in a wireless device or network node(e.g., wireless device 110 or network node 160 shown in FIG. 6).Apparatus 1200 is operable to carry out the example method describedwith reference to FIG. 10 and possibly any other processes or methodsdisclosed herein. It is also to be understood that the method of FIG. 10is not necessarily carried out solely by apparatus 1200. At least someoperations of the method can be performed by one or more other entities.

Virtual Apparatus 1200 may comprise processing circuitry, which mayinclude one or more microprocessor or microcontrollers, as well as otherdigital hardware, which may include digital signal processors (DSPs),special-purpose digital logic, and the like. The processing circuitrymay be configured to execute program code stored in memory, which mayinclude one or several types of memory such as read-only memory (ROM),random-access memory, cache memory, flash memory devices, opticalstorage devices, etc. Program code stored in memory includes programinstructions for executing one or more telecommunications and/or datacommunications protocols as well as instructions for carrying out one ormore of the techniques described herein, in several embodiments. In someimplementations, the processing circuitry may be used to cause receivingunit 1210 and decoding unit 1220, and any other suitable units ofapparatus 1200 to perform corresponding functions according one or moreembodiments of the present disclosure.

As illustrated in FIG. 12, apparatus 1200 includes receiving unit 1210and decoding unit 1220. Receiving unit 1210 is configured to receiveencoded bits, such as the information encoded according to FIG. 9.Decoding unit 1220 is configured to Polar decode the received bits usingthe parity bits described in the embodiments and examples describedabove.

Generally, all terms used herein are to be interpreted according totheir ordinary meaning in the relevant technical field, unless adifferent meaning is clearly given and/or is implied from the context inwhich it is used. All references to a/an/the element, apparatus,component, means, step, etc. are to be interpreted openly as referringto at least one instance of the element, apparatus, component, means,step, etc., unless explicitly stated otherwise. The steps of any methodsdisclosed herein do not have to be performed in the exact orderdisclosed, unless a step is explicitly described as following orpreceding another step and/or where it is implicit that a step mustfollow or precede another step. Any feature of any of the embodimentsdisclosed herein may be applied to any other embodiment, whereverappropriate. Likewise, any advantage of any of the embodiments may applyto any other embodiments, and vice versa. Other objectives, features andadvantages of the enclosed embodiments will be apparent from thefollowing description.

Those skilled in the art will recognize improvements and modificationsto the embodiments of the present disclosure. All such improvements andmodifications are considered within the scope of the concepts disclosedherein.

REFERENCE LIST

-   [1] E. Arikan, “Channel Polarization: A Method for Constructing    Capacity-Achieving Codes for Symmetric Binary-Input Memoryless    Channels,” IEEE Transactions on Information Theory, vol. 55, pp.    3051-3073, July 2009.-   [2] I. Tal and A. Vardy, “List Decoding of polar codes,” in    Proceedings of IEEE Symp. Inf. Theory, pp. 1-5, 2011.-   [3] Leroux, et. al., “A Semi-Parallel Successive-Cancellation    Decoder for Polar Codes,” IEEE TRANSACTIONS ON SIGNAL PROCESSING,    VOL. 61, NO. 2, Jan. 15, 2013.

Abbreviations

At least some of the following abbreviations may be used in thisdisclosure. If there is an inconsistency between abbreviations,preference should be given to how it is used above. If listed multipletimes below, the first listing should be preferred over any subsequentlisting(s).

-   1×RTT CDMA2000 1× Radio Transmission Technology-   3GPP 3rd Generation Partnership Project-   5G 5th Generation-   ABS Almost Blank Subframe-   ARQ Automatic Repeat Request-   AWGN Additive White Gaussian Noise-   BCCH Broadcast Control Channel-   BCH Broadcast Channel-   CA Carrier Aggregation-   CC Carrier Component-   CCCH SDU Common Control Channel SDU-   CDMA Code Division Multiplexing Access-   CGI Cell Global Identifier-   CIR Channel Impulse Response-   CP Cyclic Prefix-   CPICH Common Pilot Channel-   CPICH Ec/No CPICH Received energy per chip divided by the power    density in the band-   CQI Channel Quality information-   C-RNTI Cell RNTI-   CSI Channel State Information-   DCCH Dedicated Control Channel-   DCI Downlink Control Information-   DFTS OFDM Discrete Fourier Transform Spread OFDM-   DL Downlink-   DM Demodulation-   DMRS Demodulation Reference Signal-   DRX Discontinuous Reception-   DTX Discontinuous Transmission-   DTCH Dedicated Traffic Channel-   DUT Device Under Test-   E-CID Enhanced Cell-ID (positioning method)-   E-SMLC Evolved-Serving Mobile Location Centre-   ECGI Evolved CGI-   eNB E-UTRAN NodeB-   ePDCCH enhanced Physical Downlink Control Channel-   E-SMLC evolved Serving Mobile Location Center-   E-UTRA Evolved UTRA-   E-UTRAN Evolved UTRAN-   FDD Frequency Division Duplex-   FFS For Further Study-   GERAN GSM EDGE Radio Access Network-   gNB Base station in NR-   GNSS Global Navigation Satellite System-   GSM Global System for Mobile communication-   HARQ Hybrid Automatic Repeat Request-   HO Handover-   HSPA High Speed Packet Access-   HRPD High Rate Packet Data-   IR-HARQ Incremental Redundancy HARQ-   LLR Log Likelihood Ratio-   LOS Line of Sight-   LPP LTE Positioning Protocol-   LTE Long-Term Evolution-   MAC Medium Access Control-   MBMS Multimedia Broadcast Multicast Services-   MBSFN Multimedia Broadcast multicast service Single Frequency    Network-   MBSFN ABS MBSFN Almost Blank Subframe-   MDT Minimization of Drive Tests-   MIB Master Information Block-   MME Mobility Management Entity-   MSC Mobile Switching Center-   NPDCCH Narrowband Physical Downlink Control Channel-   NR New Radio-   OCNG OFDMA Channel Noise Generator-   OFDM Orthogonal Frequency Division Multiplexing-   OFDMA Orthogonal Frequency Division Multiple Access-   OSS Operations Support System-   OTDOA Observed Time Difference of Arrival-   O&M Operation and Maintenance-   PBCH Physical Broadcast Channel-   P-CCPCH Primary Common Control Physical Channel-   PCell Primary Cell-   PCFICH Physical Control Format Indicator Channel-   PDCCH Physical Downlink Control Channel-   PDP Profile Delay Profile-   PDSCH Physical Downlink Shared Channel-   PGW Packet Gateway-   PHICH Physical Hybrid-ARQ Indicator Channel-   PLMN Public Land Mobile Network-   PMI Precoder Matrix Indicator-   PRACH Physical Random Access Channel-   PRS Positioning Reference Signal-   PSS Primary Synchronization Signal-   PUCCH Physical Uplink Control Channel-   PUSCH Physical Uplink Shared Channel-   RACH Random Access Channel-   QAM Quadrature Amplitude Modulation-   RAN Radio Access Network-   RAT Radio Access Technology-   RLM Radio Link Management-   RNC Radio Network Controller-   RNTI Radio Network Temporary Identifier-   RRC Radio Resource Control-   RRM Radio Resource Management-   RS Reference Signal-   RSCP Received Signal Code Power-   RSRP Reference Symbol Received Power OR    -   Reference Signal Received Power-   RSRQ Reference Signal Received Quality OR    -   Reference Symbol Received Quality-   RSSI Received Signal Strength Indicator-   RSTD Reference Signal Time Difference-   SC Successive Cancellation-   SCL Successive Cancellation List-   SCH Synchronization Channel-   SCell Secondary Cell-   SDU Service Data Unit-   SFN System Frame Number-   SGW Serving Gateway-   SI System Information-   SIB System Information Block-   SNR Signal to Noise Ratio-   SON Self Optimized Network-   SS Synchronization Signal-   SSB Synchronization Signal Block-   SSS Secondary Synchronization Signal-   TDD Time Division Duplex-   TDOA Time Difference of Arrival-   TOA Time of Arrival-   TSS Tertiary Synchronization Signal-   TTI Transmission Time Interval-   UCI Uplink Control Information-   UE User Equipment-   UL Uplink-   UMTS Universal Mobile Telecommunication System-   USIM Universal Subscriber Identity Module-   UTDOA Uplink Time Difference of Arrival-   UTRA Universal Terrestrial Radio Access-   UTRAN Universal Terrestrial Radio Access Network-   WCDMA Wide CDMA-   WLAN Wide Local Area Network

1. A method performed by a wireless transmitter for encoding informationbits, the method comprising: receiving a set of information bits;determining a set of parity check bits, wherein each parity check bit inthe set of parity check bits is the binary sum of values of all bits infront of it; concatenating the set of information bits with the set ofparity check bits; polar encoding the information bits into a set ofinformation bits and frozen bits; and transmitting the encoded set ofinformation bits to a wireless receiver.
 2. The method of claim 1,wherein each parity check bit in the set of parity check bits is thebinary sum of all bits values in front of it, except for other paritycheck bits.
 3. The method of claim 1, wherein the bits in front of eachparity check bit in the set of parity check bits includes at least onepreceding parity check bit.
 4. A method performed by a wireless receiverfor decoding information bits, the method comprising: receiving a set ofpolar coded information bits concatenated with a set of parity checkbits, wherein each parity check bit in the set of parity check bits isthe binary sum of values of all bits in front of it; decoding the set ofpolar coded information bits concatenated with the set of parity checkbits; and terminating the decoding when one of the parity check bits inthe set of parity check bits indicates an error.
 5. The method of claim4, wherein each parity check bit in the set of parity check bits is thebinary sum of the values of all bits in front of it, except for otherparity check bits.
 6. The method of claim 4, wherein the bits in frontof each parity check bit in the set of parity check bits includes atleast one preceding parity check bit.
 7. A method performed by awireless transmitter for encoding information bits, the methodcomprising: receiving a set of information bits; generating a set ofparity check bits based on a systematic block code on the least reliablebits of the set of information bits; concatenating the set ofinformation bits with the set of parity check bits; polar encoding theinformation bits into a set of information bits and frozen bits; andtransmitting the encoded set of information bits to a wireless receiver.8. A method performed by a wireless receiver for decoding informationbits, the method comprising: receiving a set of polar coded informationbits concatenated with a set of parity check bits, wherein the set ofparity check bits is generated based on a systematic block code on theleast reliable bits of the set of information bits and frozen bits;decoding the set of polar coded information bits concatenated with theset of parity check bits; and terminating the decoding when one of theparity check bits in the set of parity check bits indicates an error. 9.A wireless device for encoding information bits, the wireless devicecomprising: processing circuitry configured to perform any of the stepsof claim 1; and power supply circuitry configured to supply power to thewireless device.
 10. A base station for encoding information bits, thebase station comprising: processing circuitry configured to perform anyof the steps of claim 1; power supply circuitry configured to supplypower to the wireless device.
 11. A user equipment (UE) for encodinginformation bits, the UE comprising: an antenna configured to send andreceive wireless signals; radio front-end circuitry connected to theantenna and to processing circuitry, and configured to condition signalscommunicated between the antenna and the processing circuitry; theprocessing circuitry being configured to perform any of the steps ofclaim 1 an input interface connected to the processing circuitry andconfigured to allow input of information into the UE to be processed bythe processing circuitry; an output interface connected to theprocessing circuitry and configured to output information from the UEthat has been processed by the processing circuitry; and a batteryconnected to the processing circuitry and configured to supply power tothe UE.
 12. A computer-readable medium storing instructions thereon for,when executed by at least one processor, performing a method by awireless transmitter for encoding information bits, the methodcomprising: receiving a set of information bits; determining a set ofparity check bits, wherein each parity check bit in the set of paritycheck bits is the binary sum of values all bits in front of it;concatenating the set of information bits with the set of parity checkbits; polar encoding the information bits into a set of information bitsand frozen bits; and transmitting the encoded set of information bits toa wireless receiver.
 13. The computer-readable medium of claim 12,wherein each parity check bit in the set of parity check bits is thebinary sum of values of all bits in front of it, except for other paritycheck bits.
 14. The computer-readable medium of claim 12, wherein thebits in front of each parity check bit in the set of parity check bitsincludes at least one preceding parity check bit.
 15. Acomputer-readable medium storing instructions thereon for, when executedby at least one processor, performing a method by a wireless receiverfor decoding information bits, the method comprising: receiving a set ofpolar coded information bits concatenated with a set of parity checkbits, wherein each parity check bit in the set of parity check bits isthe binary sum of values of all bits in front of it; decoding the set ofpolar coded information bits concatenated with the set of parity checkbits; and terminating the decoding when one of the parity check bits inthe set of parity check bits indicates an error.
 16. Thecomputer-readable medium of claim 15, wherein each parity check bit inthe set of parity check bits is the binary sum of the values of all bitsvalues in front of it, except for other parity check bits.
 17. Thecomputer-readable medium of claim 15, wherein the bits in front of eachparity check bit in the set of parity check bits includes at least onepreceding parity check bit.
 18. (canceled)
 19. (canceled)